Evaluate
\frac{119500000}{11}\approx 10863636.363636364
Factor
\frac{2 ^ {5} \cdot 5 ^ {6} \cdot 239}{11} = 10863636\frac{4}{11} = 10863636.363636363
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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)119500000}\\\end{array}
Use the 1^{st} digit 1 from dividend 119500000
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)119500000}\\\end{array}
Since 1 is less than 11, use the next digit 1 from dividend 119500000 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)119500000}\\\end{array}
Use the 2^{nd} digit 1 from dividend 119500000
\begin{array}{l}\phantom{11)}01\phantom{4}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}0\\\end{array}
Find closest multiple of 11 to 11. We see that 1 \times 11 = 11 is the nearest. Now subtract 11 from 11 to get reminder 0. Add 1 to quotient.
\begin{array}{l}\phantom{11)}01\phantom{5}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}9\\\end{array}
Use the 3^{rd} digit 9 from dividend 119500000
\begin{array}{l}\phantom{11)}010\phantom{6}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}9\\\end{array}
Since 9 is less than 11, use the next digit 5 from dividend 119500000 and add 0 to the quotient
\begin{array}{l}\phantom{11)}010\phantom{7}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\end{array}
Use the 4^{th} digit 5 from dividend 119500000
\begin{array}{l}\phantom{11)}0108\phantom{8}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\phantom{11)}\underline{\phantom{99}88\phantom{99999}}\\\phantom{11)999}7\\\end{array}
Find closest multiple of 11 to 95. We see that 8 \times 11 = 88 is the nearest. Now subtract 88 from 95 to get reminder 7. Add 8 to quotient.
\begin{array}{l}\phantom{11)}0108\phantom{9}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\phantom{11)}\underline{\phantom{99}88\phantom{99999}}\\\phantom{11)999}70\\\end{array}
Use the 5^{th} digit 0 from dividend 119500000
\begin{array}{l}\phantom{11)}01086\phantom{10}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\phantom{11)}\underline{\phantom{99}88\phantom{99999}}\\\phantom{11)999}70\\\phantom{11)}\underline{\phantom{999}66\phantom{9999}}\\\phantom{11)9999}4\\\end{array}
Find closest multiple of 11 to 70. We see that 6 \times 11 = 66 is the nearest. Now subtract 66 from 70 to get reminder 4. Add 6 to quotient.
\begin{array}{l}\phantom{11)}01086\phantom{11}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\phantom{11)}\underline{\phantom{99}88\phantom{99999}}\\\phantom{11)999}70\\\phantom{11)}\underline{\phantom{999}66\phantom{9999}}\\\phantom{11)9999}40\\\end{array}
Use the 6^{th} digit 0 from dividend 119500000
\begin{array}{l}\phantom{11)}010863\phantom{12}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\phantom{11)}\underline{\phantom{99}88\phantom{99999}}\\\phantom{11)999}70\\\phantom{11)}\underline{\phantom{999}66\phantom{9999}}\\\phantom{11)9999}40\\\phantom{11)}\underline{\phantom{9999}33\phantom{999}}\\\phantom{11)99999}7\\\end{array}
Find closest multiple of 11 to 40. We see that 3 \times 11 = 33 is the nearest. Now subtract 33 from 40 to get reminder 7. Add 3 to quotient.
\begin{array}{l}\phantom{11)}010863\phantom{13}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\phantom{11)}\underline{\phantom{99}88\phantom{99999}}\\\phantom{11)999}70\\\phantom{11)}\underline{\phantom{999}66\phantom{9999}}\\\phantom{11)9999}40\\\phantom{11)}\underline{\phantom{9999}33\phantom{999}}\\\phantom{11)99999}70\\\end{array}
Use the 7^{th} digit 0 from dividend 119500000
\begin{array}{l}\phantom{11)}0108636\phantom{14}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\phantom{11)}\underline{\phantom{99}88\phantom{99999}}\\\phantom{11)999}70\\\phantom{11)}\underline{\phantom{999}66\phantom{9999}}\\\phantom{11)9999}40\\\phantom{11)}\underline{\phantom{9999}33\phantom{999}}\\\phantom{11)99999}70\\\phantom{11)}\underline{\phantom{99999}66\phantom{99}}\\\phantom{11)999999}4\\\end{array}
Find closest multiple of 11 to 70. We see that 6 \times 11 = 66 is the nearest. Now subtract 66 from 70 to get reminder 4. Add 6 to quotient.
\begin{array}{l}\phantom{11)}0108636\phantom{15}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\phantom{11)}\underline{\phantom{99}88\phantom{99999}}\\\phantom{11)999}70\\\phantom{11)}\underline{\phantom{999}66\phantom{9999}}\\\phantom{11)9999}40\\\phantom{11)}\underline{\phantom{9999}33\phantom{999}}\\\phantom{11)99999}70\\\phantom{11)}\underline{\phantom{99999}66\phantom{99}}\\\phantom{11)999999}40\\\end{array}
Use the 8^{th} digit 0 from dividend 119500000
\begin{array}{l}\phantom{11)}01086363\phantom{16}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\phantom{11)}\underline{\phantom{99}88\phantom{99999}}\\\phantom{11)999}70\\\phantom{11)}\underline{\phantom{999}66\phantom{9999}}\\\phantom{11)9999}40\\\phantom{11)}\underline{\phantom{9999}33\phantom{999}}\\\phantom{11)99999}70\\\phantom{11)}\underline{\phantom{99999}66\phantom{99}}\\\phantom{11)999999}40\\\phantom{11)}\underline{\phantom{999999}33\phantom{9}}\\\phantom{11)9999999}7\\\end{array}
Find closest multiple of 11 to 40. We see that 3 \times 11 = 33 is the nearest. Now subtract 33 from 40 to get reminder 7. Add 3 to quotient.
\begin{array}{l}\phantom{11)}01086363\phantom{17}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\phantom{11)}\underline{\phantom{99}88\phantom{99999}}\\\phantom{11)999}70\\\phantom{11)}\underline{\phantom{999}66\phantom{9999}}\\\phantom{11)9999}40\\\phantom{11)}\underline{\phantom{9999}33\phantom{999}}\\\phantom{11)99999}70\\\phantom{11)}\underline{\phantom{99999}66\phantom{99}}\\\phantom{11)999999}40\\\phantom{11)}\underline{\phantom{999999}33\phantom{9}}\\\phantom{11)9999999}70\\\end{array}
Use the 9^{th} digit 0 from dividend 119500000
\begin{array}{l}\phantom{11)}010863636\phantom{18}\\11\overline{)119500000}\\\phantom{11)}\underline{\phantom{}11\phantom{9999999}}\\\phantom{11)99}95\\\phantom{11)}\underline{\phantom{99}88\phantom{99999}}\\\phantom{11)999}70\\\phantom{11)}\underline{\phantom{999}66\phantom{9999}}\\\phantom{11)9999}40\\\phantom{11)}\underline{\phantom{9999}33\phantom{999}}\\\phantom{11)99999}70\\\phantom{11)}\underline{\phantom{99999}66\phantom{99}}\\\phantom{11)999999}40\\\phantom{11)}\underline{\phantom{999999}33\phantom{9}}\\\phantom{11)9999999}70\\\phantom{11)}\underline{\phantom{9999999}66\phantom{}}\\\phantom{11)99999999}4\\\end{array}
Find closest multiple of 11 to 70. We see that 6 \times 11 = 66 is the nearest. Now subtract 66 from 70 to get reminder 4. Add 6 to quotient.
\text{Quotient: }10863636 \text{Reminder: }4
Since 4 is less than 11, stop the division. The reminder is 4. The topmost line 010863636 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 10863636.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}